An obstruction for the mean curvature of a conformal immersion 𝑆ⁿ→ℝⁿ⁺¹

DOI10.1090/S0002-9939-06-08491-7zbMath1106.53035arXivmath/0506568MaRDI QIDQ3420018

Emmanuel Humbert, Bernd Ammann, Mohameden Ould Ahmedou

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506568

zbMATH Keywords

scalar curvaturemean curvaturenonlinear eigenvalue equationsKazdan-Warner obstruction

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Nonlinear elliptic equations (35J60) Spin and Spin({}^c) geometry (53C27)

Related Items (11)

A perturbation method for spinorial Yamabe type equations on \(S^m\) and its application ⋮ An obstruction to the existence of immersed curves of prescribed curvature ⋮ Curvature effect in the spinorial Yamabe problem on product manifolds ⋮ Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations ⋮ A variational analysis of the spinorial Yamabe equation on product manifolds ⋮ Infinitely many solutions for the spinorial Yamabe problem on the round sphere ⋮ Green functions for the Dirac operator under local boundary conditions and applications ⋮ Conformal immersions of prescribed mean curvature in \(\mathbb{R}^3\) ⋮ Spinorial Yamabe Type Equations on S³ via Conley Index ⋮ A Sobolev-like inequality for the Dirac operator ⋮ UNIVERSAL PRINCIPLES FOR KAZDAN–WARNER AND POHOZAEV–SCHOEN TYPE IDENTITIES

Cites Work

• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
• Scalar curvature and conformal deformation of Riemannian structure
• Extrinsic bounds for eigenvalues of the Dirac operator
• On the spinor representation of surfaces in Euclidean \(3\)-space
• Harmonic spinors
• Scalar Curvature Functions in a Conformal Class of Metrics and Conformal Transformations
• Unnamed Item

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